AI 中文总结
本文综述空间均匀宇宙学中的奇点实现，区分物质奇点与whimper奇点，并回顾Ellis-King分析及后续发展，揭示奇点边界的丰富层级。
AI 中文摘要
本文是一篇关于经典广义相对论中时空奇点的综述的第二部分。虽然《入门 I》发展了用于定义、分类和证明奇点存在的数学框架，但当前工作考察了它们在空间均匀宇宙学模型中的具体实现。在回顾了均匀性的几何基础和 Bianchi 分类之后，我们推导了正交和倾斜理想流体宇宙学的场方程，并使用 Kasner 和 Bianchi I 解作为各向异性奇点行为的基本原型。Raychaudhuri 聚焦提供了均匀 Cauchy 发展达到有限固有时边界的普遍条件。然后，我们将物质奇点（以密度和 Ricci 曲率发散为特征）与更微妙的非标量或 whimper 奇点（与 Cauchy 视界和极端流体倾斜相关）区分开来。经典的 Ellis-King 分析在后续发展的背景下被重新审视，包括 Bianchi VIII 和 IX 模型的严格曲率爆破结果、测地完备倾斜时空中的运动学奇点，以及偶极宇宙学中 whimper 行为的最近重现。由此产生的图景表明，即使是空间均匀宇宙学也展现出显著丰富的奇点边界层级。对这些边界的详细动力学方法——Hamiltonian 宇宙学、Kasner 跃迁、Mixmaster 动力学和 BKL 猜想——将留给《入门 III》。
英文摘要
This article is the second part of a review devoted to spacetime singularities in classical General Relativity. While Primer I developed the mathematical framework for defining, classifying, and proving the existence of singularities, the present work examines their concrete realization in spatially homogeneous cosmological models. After reviewing the geometrical foundations of homogeneity and the Bianchi classification, we derive the field equations for orthogonal and tilted perfect fluid cosmologies and use the Kasner and Bianchi I solutions as elementary prototypes of anisotropic singular behaviour. Raychaudhuri focusing provides general conditions under which the homogeneous Cauchy development reaches a finite proper time boundary. We then distinguish matter singularities, characterized by divergent density and Ricci curvature, from more subtle non-scalar or whimper singularities associated with Cauchy horizons and extreme fluid tilt. The classical Ellis-King analysis is reconsidered in the light of later developments, including rigorous curvature-blow-up results for Bianchi VIII and IX models, kinematic singularities in geodesically complete tilted spacetimes, and the recent reappearance of whimper behaviour in dipole cosmology. The resulting picture shows that even spatially homogeneous cosmologies exhibit a remarkably rich hierarchy of singular boundaries. The detailed dynamical approach to these boundaries - Hamiltonian cosmology, Kasner transitions, Mixmaster dynamics and the BKL conjecture - is reserved for Primer III.
Comments43 pages, 4 figures, Appendix
